CAMBRIDGE, Md. — House Republicans may again tie a debt ceiling increase to a repeal of a section of President Barack Obama's health care law, but the plan remains murky after a three-day retreat here.

At an afternoon panel moderated by GOP leaders and former Congressional Budget Office Director Doug Holtz-Eakin, members expressed support for tying a one-year increase to the nation's borrowing limit to a repeal of the health law's so called risk corridors, a provision that mitigates risk for insurance companies.

"That’s certainly was an option put forward by some members," said Rep. Jim Jordan, R-Ohio, who last year helped craft the GOP's debt ceiling strategy. The calculation for leadership is whether they can draw 218 Republican votes for the plan, which would almost certainly be rejected by a majority of Democrats. Any increase to the debt ceiling will be a heavy lift, especially during an election year in which members can draw primary ire for supporting a policy that is generally unpopular among Republican constituency.

But tying the increase to the risk corridor plan drew some unexpected support. Rep. Michele Bachmann, R-Minn., for instance, surprised leadership when said she would vote for the increase, according to a member in the room.

Other plans emerged, such as tying the increase to a balanced budget amendment to the Constitution or language that would spur the Keystone XL oil pipeline project. But the risk corridor repeal seemed to have the most support, said Rep. Tom Cole, R-Okla.

He noted the plan would not be accepted by Democrats, but if Republicans can pass it, it could be on opening bid in negotiations. Last year, he said, Republicans raised the debt ceiling in exchange for a plan that forced the Senate to write a budget.

"People called it gimmicky, but guess what? The Senate produced a budget. ... That was the beginning of something that turned out pretty good, for all concerned," he said. "If the Democrats don’t accept it, OK, the process may yield something we don’t expect."